Point estimation, confidence intervals, and P-values for optimal adaptive two-stage designs with normal endpoints.

Due to the dependency structure in the sampling process, adaptive trial designs create challenges in point and interval estimation and in the calculation of P-values. Optimal adaptive designs, which are designs where the parameters governing the adaptivity are chosen to maximize some performance criterion, suffer from the same problem. Various analysis methods which are able to handle this dependency structure have already been developed. In this work, we aim to give a comprehensive summary of these methods and show how they can be applied to the class of designs with planned adaptivity, of which optimal adaptive designs are an important member. The defining feature of these kinds of designs is that the adaptive elements are completely prespecified. This allows for explicit descriptions of the calculations involved, which makes it possible to evaluate different methods in a fast and accurate manner. We will explain how to do so, and present an extensive comparison of the performance characteristics of various estimators between an optimal adaptive design and its group-sequential counterpart.

Point estimation for adaptive trial designs I: A methodological review.

Recent FDA guidance on adaptive clinical trial designs defines bias as "a systematic tendency for the estimate of treatment effect to deviate from its true value," and states that it is desirable to obtain and report estimates of treatment effects that reduce or remove this bias. The conventional end-of-trial point estimates of the treatment effects are prone to bias in many adaptive designs, because they do not take into account the potential and realized trial adaptations. While much of the methodological developments on adaptive designs have tended to focus on control of type I error rates and power considerations, in contrast the question of biased estimation has received relatively less attention. This article is the first in a two-part series that studies the issue of potential bias in point estimation for adaptive trials. Part I provides a comprehensive review of the methods to remove or reduce the potential bias in point estimation of treatment effects for adaptive designs, while part II illustrates how to implement these in practice and proposes a set of guidelines for trial statisticians. The methods reviewed in this article can be broadly classified into unbiased and bias-reduced estimation, and we also provide a classification of estimators by the type of adaptive design. We compare the proposed methods, highlight available software and code, and discuss potential methodological gaps in the literature.

Adjusting for treatment selection in phase II/III clinical trials with time to event data.

Phase II/III clinical trials are efficient two-stage designs that test multiple experimental treatments. In stage 1, patients are allocated to the control and all experimental treatments, with the data collected from them used to select experimental treatments to continue to stage 2. Patients recruited in stage 2 are allocated to the selected treatments and the control. Combined data of stage 1 and stage 2 are used for a confirmatory phase III analysis. Appropriate analysis needs to adjust for selection bias of the stage 1 data. Point estimators exist for normally distributed outcome data. Extending these estimators to time to event data is not straightforward because treatment selection is based on correlated treatment effects and stage 1 patients who do not get events in stage 1 are followed-up in stage 2. We have derived an approximately uniformly minimum variance conditional unbiased estimator (UMVCUE) and compared its biases and mean squared errors to existing bias adjusted estimators. In simulations, one existing bias adjusted estimator has similar properties as the practically unbiased UMVCUE while the others can have noticeable biases but they are less variable than the UMVCUE. For confirmatory phase II/III clinical trials where unbiased estimators are desired, we recommend the UMVCUE or the existing estimator with which it has similar properties.

Point estimation for adaptive trial designs II: Practical considerations and guidance.

In adaptive clinical trials, the conventional end-of-trial point estimate of a treatment effect is prone to bias, that is, a systematic tendency to deviate from its true value. As stated in recent FDA guidance on adaptive designs, it is desirable to report estimates of treatment effects that reduce or remove this bias. However, it may be unclear which of the available estimators are preferable, and their use remains rare in practice. This article is the second in a two-part series that studies the issue of bias in point estimation for adaptive trials. Part I provided a methodological review of approaches to remove or reduce the potential bias in point estimation for adaptive designs. In part II, we discuss how bias can affect standard estimators and assess the negative impact this can have. We review current practice for reporting point estimates and illustrate the computation of different estimators using a real adaptive trial example (including code), which we use as a basis for a simulation study. We show that while on average the values of these estimators can be similar, for a particular trial realization they can give noticeably different values for the estimated treatment effect. Finally, we propose guidelines for researchers around the choice of estimators and the reporting of estimates following an adaptive design. The issue of bias should be considered throughout the whole lifecycle of an adaptive design, with the estimation strategy prespecified in the statistical analysis plan. When available, unbiased or bias-reduced estimates are to be preferred.

An Automated TW3-RUS Bone Age Assessment Method with Ordinal Regression-Based Determination of Skeletal Maturity.

The assessment of bone age is important for evaluating child development, optimizing the treatment for endocrine diseases, etc. And the well-known Tanner-Whitehouse (TW) clinical method improves the quantitative description of skeletal development based on setting up a series of distinguishable stages for each bone individually. However, the assessment is affected by rater variability, which makes the assessment result not reliable enough in clinical practice. The main goal of this work is to achieve a reliable and accurate skeletal maturity determination by proposing an automated bone age assessment method called PEARLS, which is based on the TW3-RUS system (analysis of the radius, ulna, phalanges, and metacarpal bones). The proposed method comprises the point estimation of anchor (PEA) module for accurately localizing specific bones, the ranking learning (RL) module for producing a continuous stage representation of each bone by encoding the ordinal relationship between stage labels into the learning process, and the scoring (S) module for outputting the bone age directly based on two standard transform curves. The development of each module in PEARLS is based on different datasets. Finally, corresponding results are presented to evaluate the system performance in localizing specific bones, determining the skeletal maturity stage, and assessing the bone age. The mean average precision of point estimation is 86.29%, the average stage determination precision is 97.33% overall bones, and the average bone age assessment accuracy is 96.8% within 1 year for the female and male cohorts.

A comparison of estimation methods adjusting for selection bias in adaptive enrichment designs with time-to-event endpoints.

Adaptive enrichment designs in clinical trials have been developed to enhance drug developments. They permit, at interim analyses during the trial, to select the sub-populations that benefits the most from the treatment. Because of this selection, the naive maximum likelihood estimation of the treatment effect, commonly used in classical randomized controlled trials, is biased. In the literature, several methods have been proposed to obtain a better estimation of the treatments' effects in such contexts. To date, most of the works have focused on normally distributed endpoints, and some estimators have been proposed for time-to-event endpoints but they have not all been compared side-by-side. In this work, we conduct an extensive simulation study, inspired by a real case-study in heart failure, to compare the maximum-likelihood estimator (MLE) with an unbiased estimator, shrinkage estimators, and bias-adjusted estimators for the estimation of the treatment effect with time-to-event data. The performances of the estimators are evaluated in terms of bias, variance, and mean squared error. Based on the results, along with the MLE, we recommend to provide the unbiased estimator and the single-iteration bias-adjusted estimator: the former completely eradicates the selection bias, but is highly variable with respect to a naive estimator; the latter is less biased than the MLE estimator and only slightly more variable.

Preliminary Validation of a Two-Point Estimation Task for the Measurement of Sensory Dissociation in Patients with Chronic Low Back Pain.

OBJECTIVES: Sensory dissociation (SEDI), the discrepancy between perception and actual size or shape of a painful body part, is a frequently observed finding in patients with chronic low back pain. However, the current methods of evaluating SEDI have several limitations, such as a qualitative nature and weak evidence supporting their reliability. In the current study, the reliability of two versions (manual and verbal) of a novel test, a two-point estimation task (TPE), was investigated. METHODS: To perform the manual version of the task, patients estimated the distance between two tactile stimuli delivered to their back using callipers, whereas in the verbal version they verbally reported the estimated distance. RESULTS: The manual version of TPE showed greater interexaminer reliability than the verbal version, and the mean of the two repeated measurements was sufficient for reaching excellent reliability for the pain-free (intraclass correlation coefficient [ICC] = 0.91, 95% confidence interval [CI] = 0.77-0.97) and painful (ICC = 0.86, 95% CI = 0.65-0.94) sides. Intra-examiner reliability was moderate to excellent (ICC = 0.66-0.96) for the manual version performed at the pain-free and painful sides. Distribution, duration, and intensity of pain significantly predicted SEDI and accounted for 42% of the total variance (corrected R2 = 0.42, P < 0.01). CONCLUSIONS: TPE showed higher reliability coefficients compared with tools previously suggested in the literature and can therefore be used clinically and experimentally by one or more examiners. Further research is required to investigate the validity of this new test.

Point estimation in adaptive enrichment designs.

Adaptive enrichment designs are an attractive option for clinical trials that aim at demonstrating efficacy of therapies, which may show different benefit for the full patient population and a prespecified subgroup. In these designs, based on interim data, either the subgroup or the full population is selected for further exploration. When selection is based on efficacy data, this introduces bias to the commonly used maximum likelihood estimator. For the situation of two-stage designs with a single prespecified subgroup, we present six alternative estimators and investigate their performance in a simulation study. The most consistent reduction of bias over the range of scenarios considered was achieved by a method combining the uniformly minimum variance conditionally unbiased estimator with a conditional moment estimator. Application of the methods is illustrated by a clinical trial example.

Estimation of the Coefficient of Variation with Minimum Risk: A Sequential Method for Minimizing Sampling Error and Study Cost.

The coefficient of variation is an effect size measure with many potential uses in psychology and related disciplines. We propose a general theory for a sequential estimation of the population coefficient of variation that considers both the sampling error and the study cost, importantly without specific distributional assumptions. Fixed sample size planning methods, commonly used in psychology and related fields, cannot simultaneously minimize both the sampling error and the study cost. The sequential procedure we develop is the first sequential sampling procedure developed for estimating the coefficient of variation. We first present a method of planning a pilot sample size after the research goals are specified by the researcher. Then, after collecting a sample size as large as the estimated pilot sample size, a check is performed to assess whether the conditions necessary to stop the data collection have been satisfied. If not an additional observation is collected and the check is performed again. This process continues, sequentially, until a stopping rule involving a risk function is satisfied. Our method ensures that the sampling error and the study costs are considered simultaneously so that the cost is not higher than necessary for the tolerable sampling error. We also demonstrate a variety of properties of the distribution of the final sample size for five different distributions under a variety of conditions with a Monte Carlo simulation study. In addition, we provide freely available functions via the MBESS package in R to implement the methods discussed.

Using Mean Absolute Relative Phase, Deviation Phase and Point-Estimation Relative Phase to Measure Postural Coordination in a Serial Reaching Task.

The objectives of this communication are to present the methods used to calculate mean absolute relative phase (MARP), deviation phase (DP) and point estimate relative phase (PRP) and compare their utility in measuring postural coordination during the performance of a serial reaching task. MARP and DP are derived from continuous relative phase time series representing the relationship between two body segments or joints during movements. MARP is a single measure used to quantify the coordination pattern and DP measures the stability of the coordination pattern. PRP also quantifies coordination patterns by measuring the relationship between the timing of maximal or minimal angular displacements of two segments within cycles of movement. Seven young adults practiced a bilateral serial reaching task 300 times over 3 days. Relative phase measures were used to evaluate inter-joint relationships for shoulder-hip (proximal) and hip-ankle (distal) postural coordination at early and late learning. MARP, PRP and DP distinguished between proximal and distal postural coordination. There was no effect of practice on any of the relative phase measures for the group, but individual differences were seen over practice. Combined, MARP and DP estimated stability of in-phase and anti-phase postural coordination patterns, however additional qualitative movement analyses may be needed to interpret findings in a serial task. We discuss the strengths and limitations of using MARP and DP and compare MARP and DP to PRP measures in assessing coordination patterns in the context of various types of skillful tasks. Key pointsMARP, DP and PRP measures coordination between segments or joint anglesAdvantages and disadvantages of each measure should be considered in relationship to the performance taskMARP and DP may capture coordination patterns and stability of the patterns during discrete tasks or phases of movements within a taskPRP and SD or PRP may capture coordination patterns and stability during continuous oscillating movement tasks.

Point estimation of the 100p percent lethal dose using a novel penalised likelihood approach.

Estimation of the 100p percent lethal dose (LD100p) is of great interest to pharmacologists for assessing the toxicity of certain compounds. However, most existing literature focuses on the interval estimation of LD100p and little attention has been paid to its point estimation. Currently, the most commonly used method for estimating the LD100p is the maximum likelihood estimator (MLE), which can be represented as a ratio estimator, with the denominator being the slope estimated from the logistic regression model. However, the MLE can be seriously biased when the sample size is small, a common nature in such studies, or when the dose-response curve is relatively flat (i.e. the slope approaches zero). In this study, we address these issues by developing a novel penalised maximum likelihood estimator (PMLE) that can prevent the denominator of the ratio from being close to zero. Similar to the MLE, the PMLE is computationally simple and thus can be conveniently used in practice. Moreover, with a suitable penalty parameter, we show that the PMLE can (a) reduce the bias to the second order with respect to the sample size and (b) avoid extreme estimates. Through simulation studies and real data applications, we show that the PMLE generally outperforms the existing methods in terms of bias and root mean square error.

Key-point estimation of knee X-ray images using a parallel fusion decoding network.

BACKGROUND: High tibial osteotomy (HTO) is a knee preservation procedure used to treat osteoarthritis of the knee. Identifying the hinge point, surgical point, and Fujisawa point in the patient's knee X-ray before surgery is a critical task. The aim of this study was to propose an artificial intelligence-based method to effectively help surgeons select the location of these landmark points, which provides important reference for subsequent surgery. METHODS: We proposed PFDNet (parallel fusion decoding network), a novel convolutional neural network for key-point estimation of knee X-rays. PFDNet employs Res2Net for feature extraction in the network encoding phase and two partial decoders connected in parallel in the network decoding phase to finely aggregate the multiscale feature information produced by Res2Net. A total of 1842 knee X-ray images were trained, validated and predicted by PFDNet to determine whether the network could accurately detect key-points in the HTO surgical plan. RESULTS: At the hinge point, surgical point, and Fujisawa point, the average error and standard deviation from the calibration value in the PFDNet test results were 2.06 ± 1.165 mm, 2.713 ± 1.457 mm, and 2.015 ± 1.304 mm, respectively. This method exhibits superior performance compared with four convolutional neural network models that are also based on encoding and decoding frameworks: U-Net, ResUnet, SegNet, and FCN. CONCLUSION: The hinge point, surgical point, and Fujisawa point can be clearly selected by PFDNet from knee X-ray images and is locked to the millimeter level. The results show that the proposed artificial intelligence-based strategy can be instrumental in preoperative HTO planning.

Inter- and Intra-Examiner Reliability Study of Two-Point Discrimination Test (TPD) and Two-Point Estimation Task (TPE) in the Sacral Area of Pain-Free Individuals.

Tactile acuity is typically measured by a two-point discrimination test (TPD) and a two-point estimation task (TPE). In the back area, they are only conducted in the lumbar and cervical regions of the spine. Considering that such measurements have not been conducted in the sacral regions, the purpose of this study was to assess the inter- and intra-examiner reliability of the TPD and TPE at the level of the S3 segment. The study included 30 pain-free subjects aged 20-30 years. Tests were performed with a pair of stainless hardened digital calipers. The TPD was measured in two locations: 5 and 15 cm from the midline; for TPE both, points were located inside the measured area. Session 1 involved assessments by two examiners in 10-min intervals. Session 2 was measured by one examiner, at analogous intervals between tests. The TPD inter-rater reliability was excellent for mean measurements (ICC3.2: 0.76-0.8; ICC3.3: 0.8-0.92); the intra-rater reliability was excellent for mean measurements (ICC2.2: 0.79-0.85; ICC2.3: 0.82-0.86). The TPE inter-rater reliability was good to excellent for mean measurements (ICC3.2: 0.65-0.92; ICC3.3: 0.73-0.94); the intra-rater reliability for all studies (ICC2.1, ICC2.2, ICC2.3) was excellent (0.85-0.89). Two measurements are sufficient to achieve good reliability (ICC ≥ 0.75), regardless of the assessed body side.

Sensor fusion of monocular cameras and laser rangefinders for line-based Simultaneous Localization and Mapping (SLAM) tasks in autonomous mobile robots.

This paper presents a sensor fusion strategy applied for Simultaneous Localization and Mapping (SLAM) in dynamic environments. The designed approach consists of two features: (i) the first one is a fusion module which synthesizes line segments obtained from laser rangefinder and line features extracted from monocular camera. This policy eliminates any pseudo segments that appear from any momentary pause of dynamic objects in laser data. (ii) The second characteristic is a modified multi-sensor point estimation fusion SLAM (MPEF-SLAM) that incorporates two individual Extended Kalman Filter (EKF) based SLAM algorithms: monocular and laser SLAM. The error of the localization in fused SLAM is reduced compared with those of individual SLAM. Additionally, a new data association technique based on the homography transformation matrix is developed for monocular SLAM. This data association method relaxes the pleonastic computation. The experimental results validate the performance of the proposed sensor fusion and data association method.

Comparison of reliability and efficiency of two modified two-point discrimination tests and two-point estimation tactile acuity test.

Objectives: Determine reliability and minimal detectible difference of two modified two-point discrimination (TPD) testing methods and explore reliability of newer tactile acuity test, two-point estimation (TPE) method.Design: Non-experimental observational reliability study.Setting: Community.Participants: Thirty-five (female = 25) healthy individuals average age 27.7 years (SD = 9.7).Intervention: Two modified methods (i.e., descending-ascending and descending with randomization) of TPD testing utilizing decreased runs of descending and ascending measurements were tested for inter-rater reliability and efficiency between two testers at three locations (neck, hand, and foot). The newer tactile acuity test of TPE was also performed between both examiners at the three location sites.Results: Inter-rater reliability (ICC 2, k) for the descending-ascending method was 0.75, 0.79, and 0.67 for the neck, hand, and foot, respectively. For the descending with randomization method, ICC values were 0.74, 0.50, and 0.69 for the three body regions respectively. The minimal detectable difference for the neck was 28.8 and 32.7 mm, hand 5.3 and 10.8 mm, and foot 12.3 and 12.4 mm for the descending-ascending and randomization methods. TPE showed poor reliability for neck and hand (0.27 and 0.15), but moderate reliability for the foot (0.67). Time to perform the TPD test were between 54 and 108 seconds, while TPE was 12 seconds.Conclusion: The modified TPD testing methods demonstrated similar reliability to previous research, even with reduced runs allowing for increased efficiency in performing the test. The TPE method showed poor reliability, so caution should be applied when using this method.

Developing a crisis model based on higher-order moments.

In this paper, the goal is to create a model for detecting a crisis situation using the example of financial time series. An analysis of fixed and cumulative central and raw moments has been carried out. When conducting the analysis by higher-order moments, it has been shown that the moments record the presence of deviations and extreme values in the distribution of the series. Based on the higher-order moments, a crisis indicator has been proposed.

A possibilistic analogue to Bayes estimation with fuzzy data and its application in machine learning.

A Bayesian approach in a possibilistic context, when the available data for the underlying statistical model are fuzzy, is developed. The problem of point estimation with fuzzy data is studied in the possibilistic Bayesian approach introduced. For calculating the point estimation, we introduce a method without considering a loss function, and one considering a loss function. For the point estimation with a loss function, we first define a risk function based on a possibilistic posterior distribution, and then the unknown parameter is estimated based on such a risk function. Briefly, the present work extended the previous works in two directions: First the underlying model is assumed to be probabilistic rather than possibilistic, and second is that the problem of Bayes estimation is developed based on two cases of without and with considering loss function. Then, the applicability of the proposed approach to concept learning is investigated. Particularly, a naive possibility Bayes classifier is introduced and applied to some real-world concept learning problems.

Gel Point Determination in Resin Transfer Molding Process with Fiber Bragg Grating Inscribed in Side-Hole Elliptical Core Optical Fiber.

Material as well as process variations in the composites industry are reasons to develop methods for in-line monitoring, which would increase reproducibility of the manufacturing process and the final composite products. Fiber Bragg Gratings (FBGs) have shown to be useful for monitoring liquid-composite molding processes, e.g., in terms of online gel point detection. Existing works however, focus on in-plane strain measurements while out-of-plane residual strain prevails. In order to measure out-of-plane strain, FBG inscribed in highly birefringent fiber (HB FBG) can be used. The purpose of this research is the cure stage detection with (a) FBG inscribed in single mode and (b) FBG inscribed in highly-birefringent side-hole fiber in comparison to the reference gel point detected with an in-mold DC sensor. Results reveal that the curing process is better traceable with HB FBG than with regular FBG. Thus, the use of HB FBG can be a good method for the gel point estimation in the RTM process.

On evaluating the efficiency of the delta-lognormal mean estimator and predictor.

A variable taking positive values from a lognormal distribution and null values with a given probability is distributed according to the so-called delta-lognormal distribution. Two situations arise depending on whether the data are regarded as a random sample from an infinite population (superpopulation) or from a finite population, itself considered as a random sample from a superpopulation. In the case of an infinite population, estimating the mean can be accomplished using a uniformly minimum-variance unbiased estimator (UMVUE). Likewise, the prediction of the mean in the case of a finite population may be based on the UMVUE. In both cases, one expects a gain in precision when taking into account the shape of the distribution by relying on the UMVUE rather than on the sample mean, which is a nonparametric estimator (or predictor).1.For the infinite population case, the relative efficiency results presented in this article are more complete and more accurate than those published so far.2.The article fills a gap regarding the question of relative efficiency in the case of a finite population.3.Calculations were performed using the exact expression for the variance of the UMVUE of the mean, expressed in terms of the confluent hypergeometric limit function.

Estimation of change-point for a class of count time series models.

We apply a three-step sequential procedure to estimate the change-point of count time series. Under certain regularity conditions, the estimator of change-point converges in distribution to the location of the maxima of a two-sided random walk. We derive a closed-form approximating distribution for the maxima of the two-sided random walk based on the invariance principle for the strong mixing processes, so that the statistical inference for the true change-point can be carried out. It is for the first time that such properties are provided for integer-valued time series models. Moreover, we show that the proposed procedure is applicable for the integer-valued autoregressive conditional heteroskedastic (INARCH) models with Poisson or negative binomial conditional distribution. In simulation studies, the proposed procedure is shown to perform well in locating the change-point of INARCH models. And, the procedure is further illustrated with empirical data of weekly robbery counts in two neighborhoods of Baltimore City.